On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes
EPR experimental results obtained for SASeD doped with Cr³⁺ are reported with special emphasis on those observations which reveal the effect of soft modes i.e. the temperature dependence of the DZZ spin- Hamiltonian parameter and the temperature dependence of the EPR linewidth. An extension of the...
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irk-123456789-1180692017-05-29T03:03:26Z On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes Lipinski, I.E. Kuriata, J. Korynevskii, N.A. EPR experimental results obtained for SASeD doped with Cr³⁺ are reported with special emphasis on those observations which reveal the effect of soft modes i.e. the temperature dependence of the DZZ spin- Hamiltonian parameter and the temperature dependence of the EPR linewidth. An extension of the twosublattice model, previously developed and tested for SASD, to include lattice vibrations is presented. The obtained spectrum of bound excitations for the system investigated supports the idea that soft modes contribute to the phase transition at TC = 175 K. The anomaly detected at T1 = 150 K has only a quasisoft mode character and the anomaly detected at T2 = 280 K cannot be related to the effect of soft modes. Експериментальнi результати дослiджень SASeD легованого Cr³⁺ методами ЕПР поданi з наголосом на виявлений вплив м’яких мод, а саме температурної залежностi спiн-гамiльтонового параметра DZZ i ширини лiнiї ЕПР. Двопiдграткову модель, яка була запропонована i апробована раніше для SASD, узагальнено в напрямку врахування коливань гратки. Отриманий спектр зв’язаних коливань системи пiдтверджує iдею про вклад м’яких мод у фазовий перехiд при Tc = 175 K. Аномалiя, виявлена при T1 = 150 K має характер квазiм’якої моди, а аномалiю при T2 = 280 K не можна вiднести до ефекту м’яких мод. 2007 Article On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes / I.E. Lipinski, J. Kuriata, N.A. Korynevskii // Condensed Matter Physics. — 2007. — Т. 10, № 1(49). — С. 79-84. — Бібліогр.: 8 назв. — англ. 1607-324X PACS: 76.30.K, 77.80.Bh DOI:10.5488/CMP.10.1.79 http://dspace.nbuv.gov.ua/handle/123456789/118069 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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EPR experimental results obtained for SASeD doped with Cr³⁺ are reported with special emphasis on
those observations which reveal the effect of soft modes i.e. the temperature dependence of the DZZ spin-
Hamiltonian parameter and the temperature dependence of the EPR linewidth. An extension of the twosublattice
model, previously developed and tested for SASD, to include lattice vibrations is presented. The
obtained spectrum of bound excitations for the system investigated supports the idea that soft modes contribute
to the phase transition at TC = 175 K. The anomaly detected at T1 = 150 K has only a quasisoft mode
character and the anomaly detected at T2 = 280 K cannot be related to the effect of soft modes. |
| format |
Article |
| author |
Lipinski, I.E. Kuriata, J. Korynevskii, N.A. |
| spellingShingle |
Lipinski, I.E. Kuriata, J. Korynevskii, N.A. On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes Condensed Matter Physics |
| author_facet |
Lipinski, I.E. Kuriata, J. Korynevskii, N.A. |
| author_sort |
Lipinski, I.E. |
| title |
On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes |
| title_short |
On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes |
| title_full |
On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes |
| title_fullStr |
On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes |
| title_full_unstemmed |
On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes |
| title_sort |
on a correlation between epr data for sased doped with cr³⁺ and soft modes |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118069 |
| citation_txt |
On a correlation between EPR data for SASeD doped with Cr³⁺ and soft modes / I.E. Lipinski, J. Kuriata, N.A. Korynevskii // Condensed Matter Physics. — 2007. — Т. 10, № 1(49). — С. 79-84. — Бібліогр.: 8 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT lipinskiie onacorrelationbetweeneprdataforsaseddopedwithcr3andsoftmodes AT kuriataj onacorrelationbetweeneprdataforsaseddopedwithcr3andsoftmodes AT korynevskiina onacorrelationbetweeneprdataforsaseddopedwithcr3andsoftmodes |
| first_indexed |
2025-07-08T13:18:47Z |
| last_indexed |
2025-07-08T13:18:47Z |
| _version_ |
1837084943743713280 |
| fulltext |
Condensed Matter Physics 2007, Vol. 10, No 1(49), pp. 79–84
On a correlation between EPR data for SASeD doped
with Cr3+ and soft modes
I.E.Lipiński1, J.Kuriata1, N.A.Korynevskii1,2,3
1 Institute of Physics, Szczecin University of Technology, Aleja Piastów 17, 70–310 Szczecin, Poland
2 Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine,
Svientsitskii 1., 79011 Lviv, Ukraine
3 Institute of Physics, University of Szczecin, Wielkopolska 15., 70–451 Szczecin, Poland
Received September 4, 2006
EPR experimental results obtained for SASeD doped with Cr3+ are reported with special emphasis on
those observations which reveal the effect of soft modes i.e. the temperature dependence of the DZZ spin-
Hamiltonian parameter and the temperature dependence of the EPR linewidth. An extension of the two-
sublattice model, previously developed and tested for SASD, to include lattice vibrations is presented. The
obtained spectrum of bound excitations for the system investigated supports the idea that soft modes contri-
bute to the phase transition at TC = 175 K. The anomaly detected at T1 = 150 K has only a quasisoft mode
character and the anomaly detected at T2 = 280 K cannot be related to the effect of soft modes.
Key words: sodium ammonium selenate dihydrate, EPR, soft modes, phase transitions
PACS: 76.30.K, 77.80.Bh
1. Introduction
Sodium ammonium selenate dihydrate (SASeD) crystals have been investigated for many years.
Perhaps the most complete account of the properties of SASeD is given in the paper by Aleksandrov
et al. [1]. Below, we quote only a part of the information given in [1] needed for the purpose of this
paper. Below Tc = 175 K the crystal becomes ferroelectric. The transition from paraelectric phase
(with a space group P212121) to ferroelectric phase (with a space group P21) is of the first order. It
was also recognized that molecular rotations of two inequivalent groups (SeO4 (I)) and (SeO4 (II))
to a great extent contribute to the appearance of spontaneous polarization PS [2,3]. However the
effect of soft modes in the phase transition of SASeD has not been described so far. It is the aim
of this paper to report how the effect of soft modes reflects in the temperature dependence of the
EPR spectrum of SASeD doped with Cr3+ and how the theory developed by us and described in
[4] can be extended to include dipole interactions with the crystal lattice.
2. Experimental
Large and good quality single crystals of SASeD doped with Cr3+ were grown using the method
of evaporation of equimolar solution of NaNH4SeO4 and Cr(SO4) · 18H2O. The growth procedure
was kindly carried out by Prof. Czapla from Wroclaw University.
EPR spectra of the grown material were recorded using a standard EPR X-band spectrometer
with 100 kHz modulation of the steady magnetic field. The measurements were carried out in the
temperature range from 300 K down to 120 K using a liquid nitrogen cryostat.
c© I.E.Lipiński, J.Kuriata, N.A.Korynevskii 79
I.E.Lipiński, J.Kuriata, N.A.Korynevskii
3. Experimental results
The EPR spectrum of SASeD doped with Cr3+ is shown in figure 1. It could be parameterized
using a standard spin-Hamiltonian:
Ĥ = µB
~S
↔
g ~H + Ŝ
↔
D ~S (1)
with S = 3/2.
Figure 1. The EPR spectrum of SASeD:Cr3+ recorded at room temperature for ~B|z. The allowed
electronic transitions are indicated by arrows.
Temperature dependence of DZZ parameter is shown in figure 2. Three temperature points
at which the DZZ (T ) function behaves specifically can be distinguished: one about 150 K, the
other at about 175 K, and the last one at about 280 K. Obviously, the anomaly observed at 175 K
corresponds to the transition point TC. This temperature is about 5 K lower than TC determined
from dielectric measurements. The reasons for the existence of the other two anomalies can be
explained in the way it was done for sodium ammonium sulphate dehydrate (SASD) in [3].
Figure 2. Temperature dependence of the DZZ spin-Hamiltonian parameter.
The role of soft modes reflects in the temperature behaviour of DZZ below 175 K. According
to Owens [5], the softening of the phonon mode for the systems exhibiting the first order phase
transition and lacking a centre of inversion should lead to the following temperature dependence
of DZZ :
DZZ = aT ± b
√
TC − T . (2)
This type of functional dependence is seen in figure 2 in close vicinity of TC = 175 K.
Figure 3 shows the temperature dependence of the EPR linewidth for T > TC. The measure-
ments were carried out for the line corresponding to the −3/2 ↔ −1/2 electronic transition. As
80
On a correlation between EPR
Figure 3. Temperature dependence of the
EPR line for T > TC and the best fit to equa-
tion (3).
Figure 4. Temperature dependence of the
EPR line width in close vicinity of TC.
seen in figure 1, this line is distinctly separated from the rest of the spectrum and therefore it
almost perfectly suits such studies.
Figure 3 clearly shows that the linewidth broadens with the temperature decrease contrary
to the case expected for isolated Cr3+ ions in a diamagnetic host lattice. Following Owens [6]
we assumed that this phenomenon can be explained in terms of zero-field fluctuations caused by
molecular movements of polar groups. In this case, the EPR linewidth is functionally described by:
∆H = T χ(0) τC exp
(
−
E
kT
)
, (3)
where χ(0) is a low frequency limit of magnetic susceptibility, τC is correlation time. The best fit of
experimental data to the above relation enabled us to define the activation energy E = 0.0301 eV.
For T < TC the EPR linewidth should be proportional to (TC − T )
−1/2
. The temperature
dependence of the EPR linewidth in the temperature range close to TC is shown in figure 4. It
can be seen that, at least qualitatively, the experimental results support the idea of substantial
contribution of soft modes to the nature of phase transition for SASeD.
4. Theoretical considerations
In our previous paper [7] we studied in detail the contribution of two active groups SO4 (I) and
SO4 (II) to both the phase transition and to two experimentally observed anomalies for SASD.
The same Hamiltonian can be used to investigate the similar behaviour of SASeD:
H̃ = H0 + H1 , (4)
where
H0 = −
N
∑
i=1
2
∑
f=1
[
ΓfSx
fi + (∆f + p0E) Sz
fi
]
+ KSz
1iS
z
2i
, (5)
H1 = −
1
2
N
∑
ij=1
{
Jij
(
Sz
1iS
z
1j + Sz
2iS
z
2j
)
+ Kij
(
Sz
1iS
z
2j + Sz
2iS
z
1j
)}
. (6)
Here H0 describes one-particle energy and H1 describes the interaction between different par-
ticles. However, in order to include a correlation between lattice vibrations and the process of
81
I.E.Lipiński, J.Kuriata, N.A.Korynevskii
ordering occurring in the crystal under discussion one should add to (4) yet another two terms:
Hl =
∑
k,a
~ωa(~k)β+
kaβka, (7)
Hint =
∑
i,f,k,a
τafei~k ~RiSz
fi
(
βka + β+
−ka
)
. (8)
Hl corresponds to free phonon energy of the crystal lattice and Hint corresponds to pseudospin-
lattice interaction. The following designations were used in (5)–(8): i is the lattice cell number; f
is the number of sublattice (in every cell); a is the number of the branch of lattice vibration; Γ
is the tunnelling constant for motion of SeO4 group through a potential barrier; ∆f is the height
of this barrier; p0 is the dipole momentum of the active groups; E is the external electric field;
Jij , Kij are constants of interaction for particles from the same sublattice (Jij) and from different
sublattices (Kij), K = K11 = K22, ωa(~k) is the cyclic frequency of a-branch of lattice vibration
with a fixed wave vector ~k; Sx
fi, Sz
fi are spin operators, βka, β+
ka are phonon operators.
The potential barrier ∆f for the crystal structure of SASeD can be taken in the form (see [3,7]):
∆1 = ∆ + δP, ∆2 = −∆ + δP, (9)
where δ is an asymmetric constant and P is a polarization of the crystal.
In the selfconsistent field approximation H0 + H1 reduces to the following representation:
H0 + H1 =
A1 Γ Γ 0
Γ A2 0 Γ
Γ 0 A3 Γ
0 Γ Γ A4
. (10)
Here:
A1 = −K − 2(δ + J1)P − 2p0E,
A2 = K − 2∆ − 2J2ξ,
A3 = K + 2∆ + 2J2ξ,
A4 = −K + 2(δ + J1)P + 2p0E,
J1 =
∑
j
(Jij + Kij) , P =
1
2
〈Sz
1i + Sz
2i〉 ,
J2 =
∑
j
(Jij − Kij) ; ξ =
1
2
〈Sz
1i − Sz
2i〉 ;
〈. . .〉 =
Tr
[
· · · e−β(H0+H1)
]
Tr
[
e−β(H0+H1)
] , Γ = Γ1 = Γ2. (11)
Diagonalization of (4) may be obtained using a unitary transformation:
W−1 (H0 + H1) W = Hdiag, (12)
The matrix elements of W were calculated and we obtained the following pseudospin-lattice
Hamiltonian convenient for further calculations:
H =
∑
i,n
ΛnXnn
i +
∑
k,a
~ωa(~k)β+
kaβka +
∑
i,f,k,a
∑
m,n
α(f)
mnXmn
i τafei~k ~Ri
(
βka + β+
−ka
)
. (13)
In the above expression Λn are the eigenvalues of (4), Xmn
i are the Hubbard operators and
α
(1)
mn, α
(2)
mn are the matrix elements of a transformed σ̃z
f spin-like operators:
σ̃z
1 = W−1 (Sz ⊗ I) W, σ̃z
2 = W−1 (I ⊗ Sz) W ;
Sz =
(
1 0
0 −1
)
, I =
(
1 0
0 1
)
, (14)
82
On a correlation between EPR
⊗ is the symbol of a direct product.
In order to study the dynamics of a bound pseudospin-lattice system the method of double-time
Green functions [8] was used.
As a result we obtained the following relation describing the functional dependence of the bound
phonon-dipole excitations upon the temperature:
(
E2 − ~
2ω2
1
)
(E − Λmn) = 128 ~ ω1 τ2
11
(∆ + J2ξ)
2
(Λm + Λn)
2
η2
m η2
n
[
Λ2
mΛ2
n − 4 ((δ + J1) P + p0E )
2
×
(
Λ2
m + Λ2
n
)
+ 16 ((δ + J1) P + p0E)
4
]2
〈Xmm − Xnn〉 . (15)
In the above expression
ηn = 21/2
{
[
Λ2
n − 4 ((δ + J1) P + p0E)2
]2
[
Λ2
n + 4 (∆ + J2ξ)
2
]
+ 4Γ2Λ2
n
[
Λ2
n + 4 [(δ + J1)P + p0E]
2
]}1/2
. (16)
As seen in figure 5, at TC = 175 K the excitation energy (in arbitrary units) vs. T behaves in a
way typical of a soft mode (it tends to zero as T approaches TC). At T1 = 150 K the energy does
not entirely tend to zero although exhibits a clear tendency of decreasing as T approaches T1 from
the region of lower temperatures (quasisoft mode).
Figure 5. The energy of the bound lattice – active group vibrations as a function of temperature.
At T2 = 280 K one observes only a jump in the energy. This obviously does not correspond to
the behaviour typical of a soft mode.
The above facts indicate that at TC = 175 K we really observe a structural phase transition.
However, the anomalies observed at T1 = 150 K and T2 = 280 K cannot be classified as phase
transitions.
Finally, we can conclude that the anomalous behaviour of the thermodynamic functions used
in our analysis corresponds exactly to the singularities of the spectrum for collective excitations
describing the system consisting of lattice vibrations and active dipole groups.
83
I.E.Lipiński, J.Kuriata, N.A.Korynevskii
References
1. Aleksandrov K.S., Aleksandrova I.P., Zherebtsova L.I., Zaitseva M.P., Aristrotov A.T. Ferroelectrics,
1971, 2, 1–3.
2. Ramani K., Srinivasan R. Mol. Phys., 1981, 44, No. 1, 125.
3. Lipinski I.E., Korynevskii N.A., Kuriata J., Pastusiak W. Physica B, 2003, 327, 116.
4. Kuriata J., Lipinski I.E., Korynevskii N.A., Bodziony T. Physica B, 2001, 307, 203.
5. Owens F.J. Magnetic Resonance of Phase Transitions, eds. Owens F.J., Poole C.P. and Farach H.A.
Academic Press, New York, San Francisco, London, 1979.
6. Owens F.J. Phys. Status Solidi (b), 1977, 79, 623.
7. Lipinski I.E., Korynevskii N.A., Kuriata J. Ferroelectrics, 2003, 303, 217.
8. Tiablikov S.V. Methods of Quantum Theory of Magnetism. Nauka, Moscow 1975.
Про зв’язок мiж даними ЕПР для SASeD легованого Cr3+
i м’якими модами
I.Е.Лiпiньскi1, Є.Курiата1, М.А.Кориневський1,2,3
1 Iнститут фiзики, Полiтехнiка Щецiнська, Алея Пястув 17, 70–310 Щецiн, Польща
2 Iнститут фiзики конденсованих систем НАН України, Свєнцiцького 1, 79011 Львiв, Україна
3 Iнститут фiзики, Щецiнський унiверситет, Вєлькопольска 15, 70–451, Щецiн, Польща
Отримано 4 вересня 2006 р.
Експериментальнi результати дослiджень SASeD легованого Cr3+ методами ЕПР поданi з наголо-
сом на виявлений вплив м’яких мод, а саме температурної залежностi спiн-гамiльтонового параме-
тра DZZ i ширини лiнiї ЕПР. Двопiдграткову модель, яка була запропонована i апробована ранiше
для SASD, узагальнено в напрямку врахування коливань гратки. Отриманий спектр зв’язаних коли-
вань системи пiдтверджує iдею про вклад м’яких мод у фазовий перехiд при Tc = 175 K. Аномалiя,
виявлена при T1 = 150 K має характер квазiм’якої моди, а аномалiю при T2 = 280 K не можна
вiднести до ефекту м’яких мод.
Ключовi слова: натрiй-амонiєвий дигiдрат селену, ЕПР, м’якi моди, фазовi переходи
PACS: 76.30.K, 77.80.Bh
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